A thin prism P₁ with angle 4° made of glass having refractive index 1.54 , is combined with another thin prism P₂ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism P₂ in degrees is

Solution

Physics sir · 4 steps

No deviation means the two thin-prism deviations cancel, so set them equal and solve for the angle of P₂.

1. Thin prism deviation. For a thin prism of angle A and refractive index μ, the deviation is δ = (μ - 1)A.
2. No net deviation. The two prisms are placed with their bases opposite, so their deviations subtract. For zero net deviation the two deviations must be equal in size.

   (μ₁ - 1)A₁ = (μ₂ - 1)A₂

3. Put in numbers. P₁ deviates by (1.54 - 1) × 4° = 0.54 × 4° = 2.16°. So A₂ = 2.16°/(1.72 - 1) = 2.16°/0.72 = 3°.
4. So. The angle of prism P₂ is 3°, which is option (c).

The idea to keep. For dispersion without deviation, match (μ - 1)A for the two prisms. The prism with the larger μ needs the smaller angle.

Answer from the NTA final answer key. Solution by PrepWiser.